Mr Tillerson’s warning came at a hearing at the US Senate Foreign Relations Committee on Tuesday.

He said: “We are in a stage where we are moving into this next effort of ‘Are we going to have to, in effect, start taking secondary sanctions because countries we have provided information to have not, or are unwilling, or don’t have the ability to do that?'”

Washington has no trade links with North Korea, and has been considering sanctioning companies from third countries who deal with the secretive regime of Kim Jong-un in violation of UN resolutions.

However, Mr Tillerson did not name any countries.

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Image caption
North Korea has conducted a series of missile tests this year

He said the North Korea issue would be discussed with China, Pyongyang’s major ally, at a high-level talks next week.

Asked whether China has been fulfilling its pledges to put more pressure on North Korea, Mr Tillerson said: “They have taken steps, visible steps that we can confirm.”

At the committee hearing, Mr Tillerson also stated that:

The US policy of greater economic openness was providing financial support to a “very oppressive regime” in Cuba. President Trump is expected to announce tighter rules on trade and travel as early as Friday

US relations with Russia were at an “all-time low” over the conflicts in Syria and Ukraine, and also over alleged Russian meddling in the 2016 US presidential elections